What is the Greatest Common Factor of 6993 and 7000?

Greatest common factor (GCF) of 6993 and 7000 is 7.

GCF(6993,7000) = 7

We will now calculate the prime factors of 6993 and 7000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6993 and 7000.

How to find the GCF of 6993 and 7000?

We will first find the prime factorization of 6993 and 7000. After we will calculate the factors of 6993 and 7000 and find the biggest common factor number .

Step-1: Prime Factorization of 6993

Prime factors of 6993 are 3, 7, 37. Prime factorization of 6993 in exponential form is:

6993 = 3³ × 7¹ × 37¹

Step-2: Prime Factorization of 7000

Prime factors of 7000 are 2, 5, 7. Prime factorization of 7000 in exponential form is:

7000 = 2³ × 5³ × 7¹

Step-3: Factors of 6993

List of positive integer factors of 6993 that divides 6993 without a remainder.

1, 3, 7, 9, 21, 27, 37, 63, 111, 189, 259, 333, 777, 999, 2331

Step-4: Factors of 7000

List of positive integer factors of 7000 that divides 6993 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6993 and 7000. The biggest common factor number is the GCF number.
So the greatest common factor 6993 and 7000 is 7.

Also check out the Least Common Multiple of 6993 and 7000